An object is placed at a distance of `40 cm` from a concave mirror of focal length `15 cm`. If the object is displaced through a distance of `20 cm` towards the mirror, the displacement of the image will be

Options

A. `36 cm` towards the mirrorr
B. `30 cm` away from the mirrorr
C. `30cm` towards the mirrorr
D. `36 cm` away from the mirrorr

Answer

D

Explanation

In this case `u=-40cm, f=-15cm`
Using`,(1)/(v)+(1)/(u)=(1)/(f)`
`(1)/(v)+(1)/((-40))=(1)/((-15))impliesv=24cm`
Now object is displaced through a distance `20cm` towards the mirrorr
Here, `u=-20cm, f=-15 cm`
Using `,(1)/(v)+(1)/(u)=(1)/(f)`
`(1)/(v)+(1)/((-20))=(10)/((-15))impliesv=-60cm`
Hence shifting of image `Deltav=(-60)-(-24)=-36cm`
Hence image will shift `36 cm` away from mirrorr.